B.E Artificial Intelligence and Machine Learning Mathematics for Computer Engineering Syllabus - Mumbai University
This is the Second Year AI-ML syllabus under NEP 2020, in force from the academic year 2025-26. The University still sets the earlier Choice Based papers alongside it for ATKT candidates, so check which scheme your exam form names before you revise.
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Syllabus for Mathematics for Computer Engineering
Module 0: Prerequisite
- Complex Numbers, Probability, Central tendencies and dispersion in Statistical techniques, Baye’s theorem, Random variable, Discrete and Continuous random variables.
Module I: Linear Algebra (Theory of Matrices)
- 1. Characteristic Equation, Eigenvalues and Eigenvectors, and properties (without proof) 2. Cayley-Hamilton Theorem (without proof), verification and reduction of higher degree polynomials 3. Similarity of matrices, diagonalizable and non diagonalizable matrices Self-learning Topics: Derogatory and non-derogatory matrices, Functions of Square Matrix, Linear Transformations, Quadratic forms.
Module II: Linear and Non-Linear Programming Problems
- 1. Types of solutions, Standard and Canonical of LPP, Basic and Feasible solutions, slack variables, surplus variables, Simplex method. 2. NLPP with one and two equality constraint (two or three variables) using the method of Lagrange’s multipliers Self-learning Topics: Sensitivity Analysis, Big-M method, Artificial variables, Kuhn-Tucker conditions
Module III: Modular Arithmetic
- 1. Introduction to Congruence, Linear congruence, reminder theorem, solving polynomials, system of linear congruence 2. Eluer’s theorem, Fermat’s little theorem, Application of congruence-RSA algorithm. Self-learning Topics: Divisiblility, GCD, properties of prime numbers, fundamental theorem of arithmetic.
Module IV: Fourier Series
- 1. Dirichlet’s conditions, Fourier series of periodic function with period 2π and 2l. 2. Fourier series of even and odd functions. Self-learning Topics: Orthogonal and orthonormal set of functions, Complex form of Fourier Series, Half range Sine and Cosine Series.
Module V: Statistical Techniques
- 1. Karl Pearson’s coefficient of correlation (r). 2. Spearman’s Rank correlation coefficient (R) (with repeated and non-repeated ranks). 3. Lines of regression, fitting of first-degree curves. Self-learning Topics: Covariance, Fitting of second degree and exponential curve.
Module VI: Probability
- 1. Moment generating function, Raw moments. 2. Poisson Distribution, Normal Distribution Self-learning Topics: Skewness and Kurtosis of distribution (data), types of distribution and their application. must be from any other Module randomly selected from all the modules) 3. A total of Three questions needs to be answered.
Books
- 1 Higher Engineering Mathematics, Dr. B. S. Grewal, Khanna Publication.
- 2 Advanced Engineering Mathematics, Erwin Kreyszig, Wiley Eastern Limited.
- 3 Advanced Engineering Mathematics, R. K. Jain and S. R. K. Iyengar, Narosa publication
- 4 Probability, Statistics and Random Processes, T. Veerarajan, Mc. Graw Hill education.
- 5 Number theory, M. G. Nadkarni and J. S. Dani, Tata Mc. Graw Hill education.
Reproduced from the University of Mumbai syllabus for B.E. (Artificial Intelligence and Machine Learning) under NEP 2020, in force from the academic year 2025-26. Wording is as printed in that syllabus. Module numbering is as printed there too.
The complete syllabus
This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.